For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given - Maths - Polynomials

Question

For each of the following, find a quadratic polynomial whose sum
and product
respectively of the zeroes are as given Also find the zeroes
of these polynomials
by factorisation
1 -2root3 , -9
2 -3/2root5 , -1/2

Shridhar Kaushik · Accepted Answer

(1) Given that :

Sum of zeros (S) = $- 2 \sqrt{3}$

and Product of zeros (P) = – 9

∴ The required polynomial is

$p (x) = k (x^{2} - S x + P) \Rightarrow p (x) = k (x^{2} + 2 \sqrt{3} x - 9)$

where k is any non–zero real number.

To find the zeros ,

$Put p (x) = 0 \Rightarrow x^{2} + 2 \sqrt{3} x - 9 = 0 \Rightarrow x^{2} + (3 \sqrt{3} - \sqrt{3}) x - 9 = 0 \Rightarrow x^{2} + 3 \sqrt{3} x - \sqrt{3} x - 9 = 0 \Rightarrow x (x + 3 \sqrt{3}) - \sqrt{3} (x + 3 \sqrt{3}) = 0 \Rightarrow (x + 3 \sqrt{3}) (x - \sqrt{3}) = 0 \Rightarrow x + 3 \sqrt{3} = 0 or x - \sqrt{3}) = 0 \Rightarrow x = - 3 \sqrt{3} or x = \sqrt{3} Hence, the zeros are - 3 \sqrt{3} and \sqrt{3}$

(2) Similarly, you can do this query also.

If you face any problem, do get back to us.

-1

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation. 1 -2root3 , -9 2 -3/2root5 , -1/2

For each of the following, find a quadratic polynomial whose sum and product

respectively of the zeroes are as given. Also find the zeroes of these polynomials

by factorisation.

1 -2root3 , -9

2 -3/2root5 , -1/2